On the integrality ratio for tree augmentation
نویسندگان
چکیده
We show that the standard linear programming relaxation for the tree augmentation problem in undirected graphs has an integrality ratio that approaches 3 2 . This refutes a conjecture of Cheriyan, Jordán, and Ravi (ESA 1999) that the integrality ratio is 4 3 .
منابع مشابه
LP-relaxations for tree augmentation
In the Tree Augmentation problem the goal is to augment a tree T by a minimum size edge set F from a given edge set E such that T ∪ F is 2-edge-connected. The best approximation ratio known for the problem is 1.5. In the more general Weighted Tree Augmentation problem, F should be of minimum weight. Weighted Tree Augmentation admits several 2-approximation algorithms w.r.t. the standard cut-LP ...
متن کاملAn LP 7/4-approximation for the Tree Augmentation Problem
In the Tree Augmentation Problem (TAP) the goal is to augment a tree T by a minimum size edge set F from a given edge set E such that T ∪ F is 2-edge-connected. The best known approximation ratio for the problem is 1.5 [5, 12]. Several paper analysed integrality gaps of LP and SDP relaxations for the problem. In [13] is given a simple LP with gap 1.5 for the case when every edge in E connects t...
متن کاملCombinatorial 6/5-Approximation of Steiner Tree
The Steiner tree problem is one of the most fundamental and intensively studied NP-hard problems. There have been improved approximation algorithms for this problem starting from the naive 2-approximation algorithm and resulting in the best combinatorial approximation with ratio 1+ ln(3) 2 + ǫ < 1.55 [33]. An LP-based approximation algorithm, and in particular an integrality gap smaller than 2 ...
متن کاملApproximation Algorithms for Path TSP, ATSP, and TAP via Relaxations
Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman Problem (TSP) via LP relaxations. We first consider the s-t path graph-TSP, a critical special case of the metric s-t path TSP. We design a new simple LP-based algorithm for t...
متن کاملA Note on the Integrality Gap in the Nodal Interdiction Problem
In the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. In this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. Two path inequalities for the node-only interdiction problem are represented. It has been proved that the integrality gap of relaxation of the maximum fl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Oper. Res. Lett.
دوره 36 شماره
صفحات -
تاریخ انتشار 2008